# Calculating the steady-state ohmic and core losses in a BLDC Motor with temperature effects

Motors and generators with MagNetThis is an example of a Brushless DC (BLDC) Motor with Interior Permanent Magnets (IPM). The goal of the analysis is to predict the steady-state temperature of the motor and verify if the rotor magnets will demagnetize at that temperature. A 3d transient thermal analysis coupled to a 3d transient with motion magnetic analysis is used to calculate the steady-state temperature distribution after a few hours of operation. This model exhibits the typical large disparity in thermal and magnetic time constants, as the thermal time step of 20 seconds, suitable for tracking the slowly changing temperature, is much longer than the entire transient magnetic run, which is only 16.667 ms (one period of the 60 Hz AC waveform). Therefore, the coupling will perform a full 3d transient magnetic analysis between selected thermal time steps, to compute the change in performance due to increased winding resistance and degraded magnetic properties.

### METHODS and RESULTS

## MESH of ONE-EIGHT MODEL

The mesh of the one-eighth model of the BLDC IPM. Not shown is the mesh of the air region around rotor and stator, which is required for the magnetic analysis. At each transient time step in the MagNet solve the rotor mesh is rotated and the mesh in between the rotor and stator is regenerated.

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## PERIODIC BOUNDARY CONDITION

Shown in red is the periodic boundary condition that allows MagNet to take advantage of symmetry in this model. The rotor is shown rotated almost 90 degrees from its initial position.

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## END WINDINGS

The coil is designed so it doesn't intersect with its identical neighbours. Often a simpler approximation of the end windings gives good results in a magnetic simulation, but in this case, the thermal simulation requires the more detailed model, since the end windings provide most of the surface area for the convective cooling of this motor.

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## CURRENT DISTRIBUTION in WINDINGS

The current distribution in the windings is shown in this animation. Only the component of J parallel to the motor axis is shown, and since the end windings are perpendicular to this plane they show up in green (zero Jz). The rotor is made invisible except for the magnets, which give an idea of the advance phase angle.

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## CONVECTIVE LINK CALCULATOR

The most significant cooling of the rotor is by convective transfer of heat through the air gap to the stator. This cannot be modeled with a simple environmental boundary condition, but modeling the possibly turbulent fluid flow is too costly. ThermNet allows the use of an empirical model for this process, in the form of a temperature dependent convection coefficient between two surfaces. This depends on the rotor speed, Reynolds number and other properties of the fluid flow. Shown here is the calculator that generates these coefficients for a rotating machine based on the air gap geometry.

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## TEMPERATURE EFFECTS

The temperature rise during the first hour of operation shows an interesting effect. Most of the power loss and therefore heat generation is in the windings, therefore the stator temperature rises more quickly than the rotor at first. However most of the heat generated from rotor core losses ends up going through the air gap convective link to the stator, and for this to happen the rotor must be hotter than the stator.

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## FLOW OF HEAT BETWEEN ROTOR and STATOR

This video gives a much better idea of the flow of heat between rotor and stator. The scale of the shaded plot is updated continuously so that, at every time instant, the coolest part of the motor is blue and the hottest part is red.

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## RECALCULATING MAGNETIC LOSSES

A full transient magnetic 3D simulation with motion is computationally expensive, and in this case, the quantity of interest is the steady-state temperature. Therefore, this simulation does not attempt to model the actual temperature vs time. Instead, the thermal simulation is allowed to evolve until it reaches steady-state before the magnetic losses are recalculated with the updated material properties. The time instants where the magnetic losses are recalculated are clearly visible in this graph (every 2 hours of thermal time). This graph clearly illustrates the necessity of the bi-directional coupling between magnetic and thermal solvers.

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## FLUX DENSITY at the INITIAL TEMPERATURE

Shown here is the flux density at the initial temperature of 20 degrees Celsius. The flux density at the final steady-state temperature is not visibly different, but the impact on performance is significant, as explained in the next paragraph. To get the most out of this video, set the play mode to "Repeat".

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## FLUX DENSITY in the MAGNET

This graph shows the flux density in the magnet as a function of temperature (dark blue line), with the points labeled with the corresponding thermal time. Shown in red is the flux density at which the Neodymium magnet material HS-47AH starts to demagnetize. The first analysis at 20 degrees Celsius shows the magnets are far from demagnetizing. The updated material properties using first estimate of the steady-state magnet temperature (97 degrees) shows the magnets are just at the edge of demagnetization. However, the subsequent solves based on updated material properties show that the steady-state temperature reaches 116 degrees, pushing the magnets well into demagnetization.

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